The Sears Tower in Chicago is 1454 feet high. Sketch and find the angle of elevation from a point 750 feet from the base to the top of the tower. Relate your answer to the nearest tenth.
a. 62.7º
b. 27.3º
c. 31.1º
d. 58.9º
A surveyor is standing 550 feet from the base of a redwood tree in California redwood forest the tree is 362 feet tall sketch a drawing that models the situation and then find the angle of elevation of the top of the tree from the spot where the surveyor is standing
33.4
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The Sears Tower in Chicago is 1454 feet high. Sketch and find the angle of elevation from a point 750 feet from the base to the top of the tower. Relate your answer to the nearest tenth.
62.7
To find the angle of elevation from a point 750 feet from the base to the top of the Sears Tower, we can use trigonometry.
First, we can sketch a right triangle to represent the situation. Let the height of the Sears Tower be the vertical side of the triangle (1454 feet), the distance from the base to the point of observation be the horizontal side of the triangle (750 feet), and the angle of elevation be the angle opposite the height.
Next, we can use the tangent function to find the angle of elevation. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
In this case, we can use the following equation:
tan(angle of elevation) = (height of tower) / (distance from base to observation point)
tan(angle of elevation) = 1454 / 750
Using a calculator, we can find the approximate value of the tangent:
tan(angle of elevation) ≈ 1.9387
Now, we need to find the angle whose tangent is approximately 1.9387. We can use the inverse tangent function (also known as arctan or atan) to do this.
angle of elevation ≈ atan(1.9387)
Using a calculator or a table of trigonometric values, we can find the approximate angle:
angle of elevation ≈ 62.7º
Therefore, the correct answer is (a) 62.7º.